Block #169,335

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 9/17/2013, 10:28:51 PM · Difficulty 9.8683 · 6,620,558 confirmations

1CC

Cunningham Chain of the First Kind

A sequence where each prime is double the previous prime plus one.

Block Header

Block Hash

a64e08531d846a3ccf4ff79ca3a95db011953552dfc4fdea754ab5fced4f6240

View on Chainz ↗

Height

#169,335

Difficulty

9.868264

Transactions

Size

948 B

Version

Bits

09de4685

Nonce

357,204

Timestamp

9/17/2013, 10:28:51 PM

Confirmations

6,620,558

Merkle Root

65a5f1680653c5bc928c873b0bd1edc471ae3630c602d9992cf1c74598543bd6

Transactions (3)

Coinbaseadf8131bc3a3aa…054a3f85b6bf32

1 in → 1 out10.2700 XPM109 B

AXJXpeT6…EkNjftUP

19cdcadf2ed34e…53945fc442ea6e

2 in → 2 out2.0123 XPM374 B

AdiqMPgX…2U8WyDET AMmGeXac…8N1iWEtv

bf7a23126e61bc…c3e5374fb940f8

2 in → 2 out2.1980 XPM376 B

AZhT3evs…Cjwre8hG AHqZtsfn…WrCGjM3J

Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) — it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

2.452 × 10⁹¹(92-digit number)

24525729334342738095…85527343450931499039

Discovered Prime Numbers

p_k = 2^k × origin − 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

origin − 1

2.452 × 10⁹¹(92-digit number)

24525729334342738095…85527343450931499039

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

4.905 × 10⁹¹(92-digit number)

49051458668685476191…71054686901862998079

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

9.810 × 10⁹¹(92-digit number)

98102917337370952383…42109373803725996159

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

1.962 × 10⁹²(93-digit number)

19620583467474190476…84218747607451992319

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

3.924 × 10⁹²(93-digit number)

39241166934948380953…68437495214903984639

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

7.848 × 10⁹²(93-digit number)

78482333869896761907…36874990429807969279

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

1.569 × 10⁹³(94-digit number)

15696466773979352381…73749980859615938559

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

3.139 × 10⁹³(94-digit number)

31392933547958704762…47499961719231877119

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

6.278 × 10⁹³(94-digit number)

62785867095917409525…94999923438463754239

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 consecutive prime numbers forming a Cunningham Chain of the First Kind. The prime chain origin — the large number shown above — anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

★☆☆☆☆

Rarity

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 × 3 × 5 × 7 × …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial — that divisibility is part of the proof.

Prime Chain Origin = First Prime × Primorial (2·3·5·7·11·…)

Source: Primecoin prime.cpp — CheckPrimeProofOfWork()

This is why the origin has many small prime factors — those factors are the primorial divisor. The chain then extends from the first prime using the 1CC formula:

1CC: p₁ (first prime), p₂ = 2p₁ + 1, p₃ = 2p₂ + 1, …

Cross-reference on Chainz Explorer